Fungrim entry: 2d3356

\left\{ W\!\left(z\right) : z \in \mathbb{C} \setminus \mathbb{R} \right\} = \left\{ x + y i : y \in \left(-\pi, \pi\right) \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; x \in \left(-y \cot(y), \infty\right) \right\}

TeX:

\left\{ W\!\left(z\right) : z \in \mathbb{C} \setminus \mathbb{R} \right\} = \left\{ x + y i : y \in \left(-\pi, \pi\right) \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; x \in \left(-y \cot(y), \infty\right) \right\}

Definitions:

Fungrim symbol	Notation	Short description
`LambertW`	$W\!\left(z\right)$	Lambert W-function
`CC`	$\mathbb{C}$	Complex numbers
`RR`	$\mathbb{R}$	Real numbers
`ConstI`	$i$	Imaginary unit
`OpenInterval`	$\left(a, b\right)$	Open interval
`Pi`	$\pi$	The constant pi (3.14...)
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("2d3356"),
    Formula(Equal(Set(LambertW(z), ForElement(z, SetMinus(CC, RR))), Set(Add(x, Mul(y, ConstI)), For(Tuple(x, y)), And(Element(y, SetMinus(OpenInterval(Neg(Pi), Pi), Set(0))), Element(x, OpenInterval(Mul(Neg(y), Cot(y)), Infinity)))))))

Topics using this entry

Lambert W-function